Orthogonal Frequency Division Multiplexing (OFDM) is a promising transmission technology for very high-speed information transfer. It is already used in digital television broadcasts (DTVB) and wireless local area networks (WLAN). OFDM has also been proposed for fourth generation (4G) wireless communication systems and wireless asymmetric transport mode (wireless ATM).
A model of some components of a known OFDM communication system is shown in FIG. 1. FIG. 1(a) shows the structure of an OFDM transmitter. Input data S(n) (where n is an integer variable having a respective value for each symbol) to be transmitted is input (from the left of FIG. 1(a)) to a serial to parallel converter 1 to generate M parallel signals S1(n), . . . , Sk, . . . , SM(n), where the variable k in the range 1 to M labels the M elements of the n-th symbol. These signals are passed to an M-point Inverse Discrete Fourier transform (IDFT) 3. The output f(n) is transmitted to a unit 7 which adds a cyclic prefix. The result is then passed to a transmission unit 9 (e.g. a radio transmission unit in the case that the signal is to be transmitted by radio). FIG. 1(b) shows schematically how the transmitted signal (input from the left of FIG. 1(b)) is subject to a multipath channel, and to added noise. The result is received by a receiver (not shown in FIG. 1) as a serial signal y(n).
The receiver uses a serial parallel converter to remove any cyclic prefix and convert the received signal y(n) to M parallel signals y1(n), . . . , yk(n), . . . , yM(n), which we also refer to here as y(n). It then subjects the result to an M-point discrete Fourier transform (DFT), and then performs channel equalisation using an equaliser.
According to the principle of OFDM, the multipath channel can be modelled as M flat-fading channels in the frequency-domain after the DFT. Therefore the equalizer can equalize the equivalent channels, assuming that it knows the properties of the channel (here called “channel parameters”). The cyclic prefix can handle the cyclic convolution effect when the signal passes through a frequency-selective multi-path channel.
The receiver conventionally includes two independent units for respectively estimating the “carrier frequency offset” and the channel parameters. The carrier frequency offset means the frequency difference between the Inverse Discrete Fourier Transform (IDFT) in the transmitter and the Discrete Fourier Transform (DFT) in the receiver. It has respective values for all M carriers, but all depend on a single carrier frequency offset value φ. The carrier frequency offset is caused by the Doppler shift during signal transmission and the different oscillators in the transmitter and receiver. The carrier frequency offset estimation provides difference information which is input to the DFT so that the errors can be removed during the DFT process.
The channel estimator is responsible for estimating the channel parameters and providing the information to the equalizer.
We now introduce a mathematical representation of the process in the receiver.
The received signal y(n)εCM×1 can be denoted asy(n)=EWHs(n)ejφ(n−1)(M+Nc)+ξ(n)  (1)whereE=diag└1,ejφ, . . . ,ej(M−1)φ┘εCM×M  (2)is the carrier frequency offset matrix and φ is the carrier frequency offset. The term diag[ ] means a diagonal matrix having as its entries the elements of the vector in the square bracket. Nc is the length of cyclic prefix. W is the IDFT matrix. Each of its elements, corresponding to the lth row and m th column, is given by e−j2πm1/M.H=diag[h(0), . . . , h(M−1)]is the flat-fading channel parameter matrix, s(n) is a data transmitted in block n (i.e. the nth Serial-to-Parallel converting), and ξ(n)εCM×1 is an additive Gaussian noise vector.
The function of the carrier frequency offset estimation is thus to estimate E, so that its effects can be removed. Similarly, the function of the channel estimation is to estimate H, so that its effects can be removed. The estimations are performed based on received signals including a plurality of known training OFDM symbols (a “training sequence”).
In some systems, for example WLAN systems, the training sequence is a series of identical OFDM symbols. In this case, the received signal in respect of each symbol can be treated as a “sample” from the same distribution. [6] proposed a carrier frequency offset estimation using a non-linear least-square (NLS) technique, based on a cost function which is a sum over each of the training symbols (except the last) of a function of (i) the received signal for that training symbol and (ii) the received signal for the consecutively next training symbol. In other words, the cost function is generated based on relationships between “nearest neighbours” in the series of training symbols. In this way, one can estimate carrier frequency offset by N−1 statistics, where N is the number of OFDM block symbols used for the training. Moreover, the technique did not consider the relationship between the elements of the OFDM symbols.